there is a rather pronounced taper in the diameter of the case from the space in front of the belt down to the shoulder in the H&H,
which is intentional....
If you look at the H&H, and the other African "Express" rounds of the era (and before and after) you'll see nearly all of them are very tapered. ALSO, they are loaded to "moderate" pressures, not the high intensity pressures of modern magnums.
Those designers in England and on the continent were not dummies, and they knew what they were making those rounds for. AFRICA. Where temps regularly were over 100, and many preferred double rifles, so "stopping" ammo was deliberately made tapered and moderate pressure to aid in extracting fired cases.
People desiging big magnum rifle cases 50 or 100 years later had the benefit of more advanced technology (rifles and ammo) and a somewhat different primary market.
The .375 H&H is into its second century now, and while you can get things that out perform it, I wonder why you would need to...